now use the memoryless property of exponential distribution...
Have been given a challenge question to try and work out for this week, I have gotten part way through it but Im not really sure how to proceed from where I am...
So if I denote P() as a probability,Questions reads: "Let X be an exponential random variable with rate parameter λ (lambda) > 0. Suppose it is known that X > k where k is a positive constant. Given (conditional on) this, what is the probability that X > k + x? Consequently, what is the distribution of X given X > k?"
P(X > k+x) = 1 - P(X < k+x)
= 1 - F(k+x) where this is the CDF of X...
Not sure if I'm on the right track so any help would be much appreciated, Thanks!
So in in the end I worked out
= P(X>k+x)/P(X>K) = e^-(λx) = P(X > x)
So for the last part of the question how would I state the distribution?
"Consequently the distribution of X given X>k is exponential with rate λ and mean = 1/λ?"
Not sure if that's what my lecturer is meaning or not haha.